The discovery of high-temperature superconductivity in bilayer and trilayer nickelates has spurred intense interest in the Ruddlesden-Popper nickelates; yet the fundamental properties of the NiO2 layer remain obscured by interlayer coupling. It is therefore imperative to investigate the electronic properties of their single-layer counterpart — though not superconducting — to isolate the intrinsic physics of the Ni-O layer. In this work, we present a systematic study of the single-layer nickelate La1.4Sr0.6NiO4 using high-resolution angle-resolved photoemission spectroscopy (ARPES) and theoretical calculations. We reveal strong electron correlation effects, manifested by high-energy kinks in band dispersions and a pronounced orbital-dependent band renormalization. Interestingly, we observe a quasi-one-dimensional electronic structure characterized by straight Fermi surface sheets along the diagonal momentum directions. Such square-like Fermi surface topology facilitates non-Fermi liquid behavior consistent with the Luttinger liquid model, as evidenced by the power-law spectral function, robust temperature scaling, and spectroscopic features reminiscent of spin-charge separation. Our results therefore not only point toward an exotic Luttinger liquid phase emerging from the unexpected dimensional reduction in an intrinsically quasi-two-dimensional nickelate but also provide a new perspective for understanding the intriguing physics in multilayer nickelates.